Information on Result #1299128
Linear OA(3196, 6631, F3, 33) (dual of [6631, 6435, 34]-code), using construction X with Varšamov bound based on
- linear OA(3193, 6626, F3, 33) (dual of [6626, 6433, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(3177, 6562, F3, 33) (dual of [6562, 6385, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(3129, 6562, F3, 25) (dual of [6562, 6433, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(316, 64, F3, 7) (dual of [64, 48, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(3193, 6628, F3, 31) (dual of [6628, 6435, 32]-code), using Gilbert–Varšamov bound and bm = 3193 > Vbs−1(k−1) = 16 564852 206420 490003 007290 057730 577488 592014 642760 548711 847416 059609 730452 619390 865477 812379 [i]
- linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3196, 3315, F3, 2, 33) (dual of [(3315, 2), 6434, 34]-NRT-code) | [i] | OOA Folding | |